Question: Simplify the following expression: $\sqrt{6}+\sqrt{54}+\sqrt{24}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{6}+\sqrt{54}+\sqrt{24}$ $= \sqrt{6}+\sqrt{9 \cdot 6}+\sqrt{4 \cdot 6}$ Separate the radicals and simplify. $= \sqrt{6}+\sqrt{9} \cdot \sqrt{6}+\sqrt{4} \cdot \sqrt{6}$ $= \sqrt{6}+3\sqrt{6}+2\sqrt{6}$ Finally, simplify by combining the terms. $= ( 1 + 3 + 2 )\sqrt{6} = 6\sqrt{6}$